Language/Symantic/Expr/Applicative.hs

   1 {-# LANGUAGE DefaultSignatures #-}
   2 {-# LANGUAGE GADTs #-}
   3 {-# LANGUAGE FlexibleContexts #-}
   4 {-# LANGUAGE FlexibleInstances #-}
   5 {-# LANGUAGE MultiParamTypeClasses #-}
   6 {-# LANGUAGE Rank2Types #-}
   7 {-# LANGUAGE ScopedTypeVariables #-}
   8 {-# LANGUAGE TypeFamilies #-}
   9 {-# LANGUAGE TypeOperators #-}
  10 {-# LANGUAGE UndecidableInstances #-}
  11 {-# OPTIONS_GHC -fno-warn-orphans #-}
  12 -- | Expression for 'Applicative'.
  13 module Language.Symantic.Expr.Applicative where
  14
  15 import Control.Applicative (Applicative)
  16 import Data.Proxy (Proxy(..))
  17 import Data.Type.Equality ((:~:)(Refl))
  18 import Prelude hiding (Applicative(..))
  19
  20 import Language.Symantic.Type
  21 import Language.Symantic.Trans.Common
  22 import Language.Symantic.Expr.Root
  23 import Language.Symantic.Expr.Error
  24 import Language.Symantic.Expr.From
  25 import Language.Symantic.Expr.Lambda
  26 import Language.Symantic.Expr.Functor
  27
  28 -- * Class 'Sym_Applicative'
  29 -- | Symantic.
  30 class Sym_Applicative repr where
  31         pure  :: Applicative f => repr a -> repr (f a)
  32         -- (*>)  :: Applicative f => repr (f a) -> repr (f b) -> repr (f b)
  33         -- (<*)  :: Applicative f => repr (f a) -> repr (f b) -> repr (f a)
  34
  35         default pure :: (Trans t repr, Applicative f) => t repr a -> t repr (f a)
  36         pure = trans_map1 pure
  37
  38 -- * Class 'Sym_Applicative_Lam'
  39 -- | Symantic requiring a 'Lambda'.
  40 class Sym_Functor lam repr => Sym_Applicative_Lam lam repr where
  41         (<*>) :: Applicative f => repr (f (Lambda lam a b)) -> repr (f a) -> repr (f b)
  42         -- (*>)  :: Applicative f => repr (f a) -> repr (f b) -> repr (f b)
  43         -- (<*)  :: Applicative f => repr (f a) -> repr (f b) -> repr (f a)
  44
  45         default (<*>) :: (Trans t repr, Applicative f) => t repr (f (Lambda lam a b)) -> t repr (f a) -> t repr (f b)
  46         -- default (*>)  :: (Trans t, Applicative f) => t repr (f a) -> t repr (f b) -> t repr (f b)
  47         -- default (<*)  :: (Trans t, Applicative f) => t repr (f a) -> t repr (f b) -> t repr (f a)
  48         (<*>) = trans_map2 (<*>)
  49 infixl 4 <*>
  50
  51 -- * Type 'Expr_Applicative'
  52 -- | Expression.
  53 data Expr_Applicative (lam:: * -> *) (root:: *)
  54 type instance Root_of_Expr      (Expr_Applicative lam root)      = root
  55 type instance Type_of_Expr      (Expr_Applicative lam root)      = No_Type
  56 type instance Sym_of_Expr       (Expr_Applicative lam root) repr = (Sym_Applicative repr, Sym_Applicative_Lam lam repr)
  57 type instance Error_of_Expr ast (Expr_Applicative lam root)      = No_Error_Expr
  58 instance Constraint_Type1 Applicative (Type_Type0 px root)
  59 instance Constraint_Type1 Applicative (Type_Var1 root)
  60 instance Constraint_Type1 Applicative (Type_Type2 px root)
  61
  62 pure_from
  63  :: forall root ty ty_root lam ast hs ret.
  64  ( ty ~ Type_Root_of_Expr (Expr_Applicative lam root)
  65  , ty_root ~ Type_Root_of_Expr root
  66  , Eq_Type (Type_Root_of_Expr root)
  67  , Type1_from ast (Type_Root_of_Expr root)
  68  , Expr_from ast root
  69  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
  70                    (Error_of_Expr ast root)
  71  , Root_of_Expr root ~ root
  72  , Constraint_Type1 Applicative ty
  73  ) => ast -> ast
  74  -> Expr_From ast (Expr_Applicative lam root) hs ret
  75 pure_from ast_f ast_a ex ast ctx k =
  76  -- pure :: Applicative f => a -> f a
  77         either (\err -> Left $ error_expr ex $ Error_Expr_Type err ast) id $
  78         type1_from (Proxy::Proxy ty_root) ast_f $ \_f ty_f -> Right $
  79                 expr_from (Proxy::Proxy root) ast_a ctx $
  80                  \(ty_a::Type_Root_of_Expr root h_a) (Forall_Repr_with_Context a) ->
  81                 let ty_fa = ty_f ty_a in
  82                 check_constraint1_type ex (Proxy::Proxy Applicative) ast ty_fa $ \Dict ->
  83                 k ty_fa $ Forall_Repr_with_Context $
  84                  \c -> pure (a c)
  85
  86 ltstargt_from
  87  :: forall root ty lam ast hs ret.
  88  ( ty ~ Type_Root_of_Expr (Expr_Applicative lam root)
  89  , String_from_Type ty
  90  , Eq_Type (Type_Root_of_Expr root)
  91  , Eq_Type1 (Type_Root_of_Expr root)
  92  , Expr_from ast root
  93  , Lift_Type   (Type_Fun lam) (Type_of_Expr root)
  94  , Unlift_Type (Type_Fun lam) (Type_of_Expr root)
  95  , Unlift_Type1 (Type_of_Expr root)
  96  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
  97                    (Error_of_Expr ast root)
  98  , Root_of_Expr root ~ root
  99  , Constraint_Type1 Applicative ty
 100  ) => ast -> ast
 101  -> Expr_From ast (Expr_Applicative lam root) hs ret
 102 ltstargt_from ast_fg ast_fa ex ast ctx k =
 103  -- (<*>) :: Applicative f => f (a -> b) -> f a -> f b
 104         expr_from (Proxy::Proxy root) ast_fg ctx $
 105          \(ty_fg::Type_Root_of_Expr root h_fg) (Forall_Repr_with_Context fg) ->
 106         expr_from (Proxy::Proxy root) ast_fa ctx $
 107          \(ty_fa::Type_Root_of_Expr root h_fa) (Forall_Repr_with_Context fa) ->
 108         check_type1 ex ast ty_fg $ \(Type_Type1 _f (ty_g::Type_Root_of_Expr root h_g), _) ->
 109         check_type1 ex ast ty_fa $ \(Type_Type1 f ty_fa_a, Lift_Type1 ty_f) ->
 110         check_eq_type1 ex ast ty_fg ty_fa $ \Refl ->
 111         check_type_fun ex ast ty_g $ \(Type_Type2 Proxy ty_g_a ty_g_b
 112          :: Type_Fun lam (Type_Root_of_Expr root) h_g) ->
 113         check_constraint1_type ex (Proxy::Proxy Applicative) ast ty_fa $ \Dict ->
 114         check_eq_type ex ast ty_g_a ty_fa_a $ \Refl ->
 115         k (Type_Root $ ty_f $ Type_Type1 f ty_g_b) $ Forall_Repr_with_Context $
 116          \c -> (<*>) (fg c) (fa c)